Computed SAR and thermal elevation in a 0.25-mm 2 … · G. Lazzi was supported in part by the Whitaker Foundation under Contract RG-00-0298 and in part by NSF CAREER Award ECS-0091599

2274 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 9, SEPTEMBER 2003

Computed SAR and Thermal Elevation in a 0.25-mm2-D Model of the Human Eye and Head in Responseto an Implanted Retinal Stimulator—Part I: Models

and MethodsStephen C. DeMarco, Gianluca Lazzi, Senior Member, IEEE, Wentai Liu, Senior Member, IEEE,

James D. Weiland, Member, IEEE, and Mark S. Humayun, Member, IEEE

Abstract—Retinitis pigmentosa and age-related maculardegeneration lead to blindness through progressive loss of retinalphotoreceptors. Attempts are under way to construct a visualprosthesis to recover a limited sense of vision for these patientswith the aid of implantable electronic devices. The function ofthese microchips is to provide electrical stimulation to existingviable retinal tissues—living ganglion and bipolar cells—using anarray of on-chip stimulus circuits, while the dominant mechanismfor power and data communication for these implanted deviceshas been wireless inductive telemetry using coils. This paper de-scribes methods and models used to estimate the heating inducedin the human eye and surrounding head tissues subject to theoperation of this retinal prosthesis. A two-dimensional 0.25-mmhigh-resolution human head model has been developed with theaid of a new semiautomatic graphical segmentation algorithm. Fi-nite-difference-based numerical methods for both electromagneticand thermal modeling have been used to determine the influenceof the specific absorption rate (associated with 2-MHz inductivecoupling to the implant) and of stimulator integrated circuit (IC)power on tissue heating under different operational conditionsand different hypothesis on choroidal blood flow and propertiesof the complex implanted circuitry. Results, provided in Part IIof this paper, show that temperature increases of approximately0.6 and 0.4 C are induced in the midvitreous of the human eyein the absence and presence of choroidal blood flow, respectively,for a 60-electrode retinal prosthesis chip. Correspondent temper-ature rises of approximately 0.19 and 0.004C on the retina areobtained for these cases. Comparison with in vivo experimentalmeasurements on intraocular heating in dog eyes shows goodagreement.

Index Terms—Age-related macular degeneration, finite-differ-ence time domain (FDTD), retina prosthesis, retinitis pigmentosa,specific absorption rate (SAR), stimulator IC, temperature,thermal simulation.

Manuscript received November 1, 2001; revised June 3, 2002. The work ofG. Lazzi was supported in part by the Whitaker Foundation under ContractRG-00-0298 and in part by NSF CAREER Award ECS-0091599. The work ofW. Liu was supported in part by NSF Award BES-9808040 and in part by theNational Institutes of Health (NIH). The work of J. D. Weiland and M. S. Hu-mayun was supported in part by NSF Award BES-9810914 and in part by NIH.

S. C. DeMarco, G. Lazzi, and W. Liu are with the Department of Electricaland Computer Engineering, North Carolina State University, Raleigh, NC 27695USA.

J. D. Weiland and M. S. Humayun are with Doheny Eye Institute, Universityof Southern California, Los Angeles, CA 90089 USA.

Digital Object Identifier 10.1109/TAP.2003.816395

I. INTRODUCTION

A GE-RELATED macular degeneration (AMD) and retinitispigmentosa (RP), among the leading causes of blindness

[1], affect over 10 million people worldwide through progres-sive photoreceptor loss (rod/cones) in the retina [2], [3]. Thephotoreceptor cells in a healthy retina initiate a neural signal inresponse to incident light. This neural signal is further processedby bipolar and ganglion cells of the inner retina prior to deliveryto higher visual processing areas in the cortex. Retinal photore-ceptors are almost completely absent in the retina of end-stageRP and AMD patients, while the bipolar cell and ganglion cells,through which the photoreceptors normally synapse, may sur-vive at higher rates [4], [5]. The ganglion and bipolar cells re-main intact, and due to the anatomy of the retina, they are ina position where they may respond to artificially induced elec-trical stimulation via an implant. The demonstration that directelectrical stimulation of retinal ganglion cells can create visualsensation in patients has been shown clinically [6], [7]. Patientshave been able to recognize English characters and other simpleforms when stimulated by a small array of retinal electrodes.This opens the possibility of an electronic prosthesis to bypassthe defective photoreceptors.

A conceptual schematic of the retinal prosthesis system isgiven in Fig. 1. It consists of two units, extraocular and intraoc-ular. The extraocular unit includes a camera for the collection ofimages, a data encoding chip for the discretization of the imagein an 8 8 pixelized data set, and a telemetry coil for the trans-mission of power and data to the intraocular unit. The latter unitconsists of a receiving telemetry coil, a power and signal trans-ceiver and processing chip, a stimulation current driver, and astimulating electrode array mounted on the retina. The 5.55.25 mm stimulator chip occupies a central position within theeyeball so as to better isolate its heat and mechanical stressesfrom the sensitive retina, while the stimulus currents are deliv-ered to the retinal surface via the electrode array.

As with all implantable electronic devices, the operation ofthe retinal prosthesis implanted in a human patient is expectedto bring about an increase in the natural steady-state temperatureof the eye and surrounding head tissues. Therefore, a study is un-dertaken via numerical simulation to predict the extent of tem-perature increase due to the operation of the retinal prosthesis.

0018-926X/03$17.00 © 2003 IEEE

DEMARCO et al.: COMPUTED SAR AND THERMAL ELEVATION IN MODEL OF HUMAN EYE AND HEAD—PART I 2275

Fig. 1. Block diagram for the retina prosthesis system.

Ocular heating is being accounted for in terms of inductive pow-ering (for which we quantify the specific absorption rate of elec-tromagnetic power deposition) and the power dissipation in animplantable retinal stimulator microchip positioned at midvit-reous. Although the prosthesis will consist of additional com-ponents, including the receiving coil and mechanical supportstructures, our thermal studies are limited at this time to the spe-cific absorption rate (SAR) associated with inductive couplingand the power consumption in the implanted chip itself.

In recent years, studies and results have been reported inwhich the temperature increases in the head are of interest.Many of these have been brought about from the proliferationof cellular phones and concerns of their influence on the humanhead [8]–[10]. Furthermore, supposed links between electro-magnetic exposure and the formation of cataracts [11], [12]have led to increased interest in studies of thermal heating inthe human eye due to radiation in wireless computer networks[13], from infrared radiation in industrial settings [14], and toforms of electromagnetic exposure [15]. These studies havebeen primarily conducted at frequencies in the vicinity of700 MHz to 2.45 Ghz, due to the proliferation of wirelessdevices operating in these bands.

In this paper, we describe methods and models used to com-pute estimates of heating in the human eye and surroundinghead tissues subjected to the operation of such a retinal pros-thesis. Electromagnetic power deposition resulting from in-ductive telemetry and power dissipation from the implantedstimulator IC are the heating mechanisms that are characterized.

This paper is organized into seven major sections. A reviewof the numerical finite-difference time-domain (FDTD) andthermal methods is presented in Section II, accompanied by avalidation of the numerical methods against analytical deriva-tions. Section III offers comments on scaling considerations formodeling -field distribution from the three-dimensional(3-D) transmitter coil in 2-D simulation. The mathematicalmodeling of power dissipation in the stimulator IC for use inthe numerical thermal method is formulated in Section IV andcomputed in Section V. A discussion of human head and eye

model generation and the properties of the biological tissuesis provided in Sections VI and VII, respectively. The SARand thermal simulation results are presented in Part II of thispaper, along with validation according to measured data fromphysical thermal experiments.

II. COMPUTATIONAL METHODS

In order to reduce the computational complexity, the amountof required memory, and the simulation time, simulations ofelectromagnetic deposition and thermal elevation in the humanhead are conducted in two dimensions. In fact, it is possibleto approximate the fields generated by the 3-D transmitter coilused for inductive telemetry (as in the head/eye simulationsfor the retinal prosthesis) via two sources of opposite polaritynormal to a plane passing through the center of the coil andcoplanar with the coil axis.

A 2-D - transverse magnetic (TM) formulation of theFDTD method has been used to compute the induced electro-magnetic energy in a 0.25-mm resolution head model derivedfrom the visible man project (see Section VI). This- for-mulation has the advantage that the perfectly matched layer(PML) absorbing boundary conditions are independent from thebackground dielectric materials in the FDTD mesh (both in 2-Dand 3-D formulations), thus allowing the truncation of the headmodel as described in [16] in order to limit the computationalspace. The development of the method closely parallels that in[16] and [17] and for the sake of brevity will not be repeatedhere.

The thermal elevation in biological tissue can be computed bymeans of the bioheat conduction equation [13], which includesthe heating effect of basal metabolism and the cooling ef-fect of blood perfusion in the tissues. For tissue irradiatedelectromagnetically, the bioheat equation is further expanded toaccount for the heating effect of SAR, which is a measure ofabsorbed power per unit mass of tissue due to exposure to elec-tromagnetic fields and is expressed as SAR in

, for conductivity , electric field , and mass density.


Furthermore, the dissipated power of the implanted stimulatorIC is also expected to raise tissue temperature, andis included as a power density in the continuous space with unitsof W/m . The resulting expandedbioheatequation is given as

SAR

(1)where is the thermal spatial diffusion term1 for Celsiustemperature , thermal conductivity , specific heat , massdensity , and blood temperature , assumed constant at 37C.

At the boundary of the tissue where the surrounding environ-ment is encountered, the conduction of heat through the tissuearriving at the boundary normal to the surface must match theconvective transfer of heat into the environment [13]. The ex-change of heat with the surrounding environment is proportionalto the difference between the surface temperature and the envi-ronmental temperature [8], [13] as given in (2)

(2)

where is evaluated on the surface,is the surfacenormal, is the convection coefficient for heat exchangewith the environmental ambient temperature with a value of20 J/m s C [13], and is the surrounding ambient tem-perature, assumed constant at 24C. Based on the derivationfrom [13], (1) and (2) are spatially/temporally discretizedand combined as in (3) for simulation on the 2-D head/eyemodel, developed in Section VI. In particular, the SAR andstimulator IC power dissipation density are now expressed as2-D quantities in the discretized space

SAR

(3)

where is the number of interior points adjacent to cell( , ) and is the number of exterior points adjacent tocell ( , ) (i.e., those outside of the model and belonging to thesurrounding environment). The maximum time step to ensurestability of the algorithm is considered as the minimum value of

1As we are interested in temperature increases in the midvitreous (and notinternal chip temperature), we have used the termKr T instead of the moregeneralizedr(KrT ). In fact, a number of 2- and 3-D numerical tests of thechip model positioned in the center of a cylinder or a sphere have shown thatthe use of the thermal diffusion termKr T in lieu ofr(KrT ) in the 2-Dmodeling of the implanted microchip provides temperature increases that arein better agreement with those obtained outside the chip by 3-D simulationsemploying the termr(KrT ).

TABLE IPARAMETERS OF THEDISCRETIZEDBIOHEAT EQUATION

the expression of (4) [13], evaluated for all tissues and materialspresent in the discretized head/eye model

(4)

where is the set of tissues.Equations (3) and (4) are used to calculate the temperature

rise in the eye when exposed to electromagnetic radiation frominductive coupling and to power dissipation from the implantedstimulator microchip. The parameters used in these equationstogether with their units are summarized in Table I.

The accuracy of the implemented methods has been veri-fied against the analytical solution for the specific absorptionrate and the thermal response associated with a plane wave im-pacting a solid lossy cylinder, derived in [18]. The validationof our FDTD and thermal implementations is performed at thefrequency of 2.45 GHz reported in [18], in order to comparewith the published results, as well as at 2 MHz, which is theoperating frequency of the extraocular transmitting coil used toinductively power the implanted microstimulator. An excellentagreement between numerical and analytical results is obtainedfor both frequencies. Fig. 2(a) shows analytical and numericallycomputed temperature in a 10-cm-diameter cylinder exposed toa plane wave of power density 10 mW/cmat a frequency of2 MHz. The curves report the temperature at various time inter-vals subsequent to the initial irradiation time, along the diameterof the cylinder, which is perpendicular to the direction of prop-agation of the incident plane wave. The computed 2-D patternis shown in Fig. 2(b).

III. M ODELING OF THEEXTRAOCULAR COIL

As the simulations of temperature increase in the head/eyemodel developed here are conducted in two dimensions, spe-cial treatment is required for the transmitter coil. The current


(a)

(b)

Fig. 2. Temperature distribution in the test cylinder at 2-MHz irradiation. (a) Comparison of analytically and numerically computed temperature. (b) Numericallycomputed temperature distribution.

version of the telemetry system includes an extraocular trans-mitting multiturn coil of 2-in diameter located at a distance ofapproximately 2 cm from the human eye, and an intraocular re-

ceiving multiturn coil of 7-mm diameter that replaces the humanlens. The extraocular coil needs to carry a current of 2 A to de-liver the necessary power to the intraocular unit.


Fig. 3. Retina-3.5stimulator IC models discretized to 0.25-mm uniform spatial resolution.

For a low-frequency 3-D coil of radius , and turns count,, carrying a current of , we can consider the magnetic fieldas given by . The coil current in a 3-D

model space would be approximated with a finite number oftangential current vectors positioned around the circumferenceof the coil. However, for performing 2-D simulations, the coilcurrent is represented with two parallel and tangential currentvectors of opposite polarity.

This approximation requires that the theoretical value ofat the center of the multiturn external coil in the 2-D sense bescaled to that of the magnetic field at the center of the real, 3-Dcoil model. Even though the 2-D and 3-D cases are character-ized by different rates of decay of the electromagnetic field. Thishas been verified by means of 2-D and 3-D FDTD simulationsas well as by comparing analytical solutions of the electromag-netic fields generated in free space by the 2-D and 3-D approx-imations of the radiating device [19].

IV. M ODELING POWERDISSIPATION IN THESTIMULATOR IC

Modeling of the stimulator microchip also requires approxi-mations that allow us to correctly represent the power dissipatedby the chip in a 2-D space, rather than 3-D. MOSIS reports thedie size for ourRetina-3.5stimulator IC [20] in the AMI-1.2 mprocess as mm mm m. However, after ac-counting for clearance around the pad-ring for the wafer dicingsaw, the die size becomes mm mm m.

Discretizing this chip volume to 0.25-mm spatial resolutionyields the 3-D chip model shown in Fig. 3(a) with cellular di-mensions , with the total power dissi-pation expressed as a volume summation of the discrete powerdensity , as given in

(5)

When considering a 2-D model of the 3-D stimulator chipfor thermal simulation in the 2-D head/eye model of Fig. 8, the

total power is retained by integrating (or summing)the power density for the 3-D chip model along the-axis foreach cell (, ) in the 2-D chip model. Although this yields powerdensity units in 2-D of W/m, we consider that the 2-D modelshown in Fig. 3(b) can be conceptually extended infinitely in the

-dimension. Therefore units of W/mare retained in the 2-Dchip model for the power density at (, ) consistent with theunits of the tissue properties, such as mass densityin kg/m .This means of condensing the power density is formulated as

(6)

In general, the power density varies across a chip, but in thecase of ourRetina-3.5stimulator, the IC [20] consists of an arrayof 60 identical stimulus current driver circuits, which are uni-formly distributed over 75% of the chip area (25% is occupiedby digital control circuits). Thus, we approximate the powerdensity as uniformly distributed, such that

(7)

where mm, and , , and. The power density , as defined here

and associated with the 2-D chip model of Fig. 3(b), is the samevalue used in the 2-D bioheat formulation of (3).

V. COMPUTING POWERDISSIPATION IN THESTIMULATOR IC

The 60 stimulus circuits of ourRetina-3.5stimulator IC [20]provide biphasic current outputs for retinal stimulation, withprogrammable amplitudes, pulse widths, and pulse rate. Thepower consumption associated with operating the microstimu-lator can be accounted for in terms of the power dissipated in theretinal tissue (theload) plus additional power overhead requiredby the microstimulator IC. This is expressed in (8) for instanta-neous power as a function of time, where the superscript “60” inparentheses refers to the case where all 60 stimulation channels


Fig. 4. Retina-3.5stimulator IC layouts simulated inHSPICEto determine power dissipation.

are active. The subscriptschip, load,andconsumedrefer to thepower consumed in the microstimulator, retinal tissue, and thecombined system, respectively

(8)

A. Simulated Power Dissipation in the Stimulator IC

Since theRetina-3.5 stimulator IC [20] layout containsnearly 70 000 field-effect transistors, circuit simulators suchas HSPICEcannot practically conduct chip-level simulationsthat cover milliseconds of real time. However, the array ofstimulus circuits accounts for the majority of the area on our IC(about 75%). Therefore, a reasonable estimate of the dissipatedpower of the chip can be formulated from a simulation of asingle output driver (one from the array of 60), the biasingcircuit (which manifests static power dissipation), and thedigital section (associated with packet synchronization andtiming generation), designated as subcircuits X1, X2, and X3,respectively, as illustrated in Fig. 4.

In simulation, the output driver of subcircuit X1 is loadedwith a resistance to model retinal impedance[21]. The power dissipation of the chip could be predicted fromthe simulated estimates of subcircuits X1–X3, designated

Fig. 5. Parameters of the biphasic current pulse used for retinal stimulation.

as in (9), excluding the power, , dissipated in ,which is off chip

(9)

In simulating the power requirements of the stimulator IC, thestandard biphasic current pulse for retinal stimulation is consid-ered as reported in [7] and shown in Fig. 5. The microstimu-lator is programmed to produce this current waveform on all60 output channels simultaneously. Equal anodic and cathodiccurrents of 400-A (the typical case) and 600-A (the worse ormaximum case) forRetina-3.5are considered, with and


TABLE IIHSPICESIMULATED POWER DISSIPATION FOR OURRetina-3.5IC RESULTING FROM VARIATIONS IN BIPHASIC STIMULUS

Anodic and cathodic pulse amplitudes resulting fromHSPICEsimulation atV = +5 v andV = �5 v were+400.8 and�405.1�A, respectively.

Anodic and cathodic pulse amplitudes resulting fromHSPICEsimulation atV = +7 v andV = �7 v were+575.3 and�572.1�A, respectively.

The driver output stages on the stimulator IC transition from saturation to the linear region when attempting to provide 600�A for R = 10 k [21] with

V = +7 v andV = �7 v. Therefore, actual currents fall short of the requested values.

Actual frame rates are 49.827 and 60.048 Hz, derived from a 12-MHz oscillator on the extraocular communications processor, which controls stimulus timing.

Actual pulse widths are 1.023, 2.046, and 2.991 ms for 50-Hz frame rate and 1.045, 2.025, and 3.004 ms for 60-Hz frame rate again derived from the 12-MHz

oscillator.

Excludes load power.

set at v or v for each case, respectively, as appro-priate [7]. Pulse repetition rates of 50 and 60 Hz are consideredin keeping with results of flicker fusion experiments reportedin [7]. Anodic and cathodic pulse widths and interphase delaywere kept equal and varied among 1, 2, and 3 ms, consistentwith stimulation experiments also reported in [7].

These parameters are annotated as, , and on the stim-ulus waveform of Fig. 5 representing current amplitude, pulseand interphase-delay width, and period, respectively.

The subcircuits of Fig. 4 were programmed to produce thebiphasic stimulus pulse of Fig. 5 in each of the parametric com-binations described (12 cases in all). Subsequently,HSPICEsimulations were conducted to estimate the power dissipationof Retina-3.5when operating in each case. The results are tab-ulated in Table II.

When computing power estimates on semiconductor cir-cuits HSPICE considers only the power lost, or dissipated.Therefore, the estimates of from Table II are taken aslosses which would give rise to heat, and are subsequentlyused for in (7) to compute for the

thermal method in (3) to predict temperature increase in the2-D head/eye model.

B. Experimental Validation of Power Consumption andDissipation in the Stimulator IC

Experimental measurements of the microchip power con-sumption were taken to validate theHSPICEsimulations of theIC layout. Recall that our stimulator IC operates from dual dcsupply rails of and to produce the anodic and cathodicphases, respectively, with respect to a central ground return

. Therefore, an experimental estimate of chip power can be

inferred from a measurement of the power consumption minuspower dissipation in the 60 loads, as in (10)

(10)

where and are the average supply currents for theand supplies and is the rms voltage measured acrossthe load resistance, . Results of the measure-ment experiment along with the inferred microstimulator powerare summarized in Table III. A comparison between the simu-lated and measured estimates for the chip power is included. Thedifference between the simulated and experimental estimates ofthe power dissipation varies by no more than about 2 mW, thusindicating that the experimental measurement is in good agree-ment with the simulated estimates.

VI. HEAD AND EYE COMPUTATIONAL MODELS

Since the determination of a detailed thermal distribution inthe human eye is critical for the development of a safe retinalprosthesis implant, there is the need to develop a high-resolution2-D head model that accurately accounts for all the anatomicalfeatures of the human eye. Since there are no available magneticresonance images accurate enough to capture the finest anatom-ical details of the human eye, it has been necessary to derivethe eye model from an anatomically accurate sketch of a humaneye, taken from [22] and [23].

The sketch of the eye was electronically scanned to obtain animage of roughly 600 600 pixel resolution. Subsequently, theoptic nerve and the muscles connecting to the sclera were re-moved, and the resulting image was color segmented accordingto the distinct tissues represented, as shown in Fig. 6(a).

A software application has been developed to discretize thesegmented eye image onto a uniform grid of 0.25-mm resolu-tion in order to sample it to a high resolution for construction of


TABLE IIIEXPERIMENTALLY MEASUREDPOWERCONSUMPTION ANDDISSIPATION IN OUR Retina-3.5IC RESULTING FROM VARIATIONS IN BIPHASIC STIMULUS

Due to limitations in the current fabrication of ourRetina-3.5stimulator IC, operation atV = +7 v, V = �7 v yields an amplitude imbalance measured

between anodic and cathodic current when programmed to match. Therefore, experimentally measured power consumption and dissipation for validation with the

simulated data of Table II were conducted only for the cases ofV = +5 v, V = �5 v, which the matching is acceptable.

Anodic and cathodic pulse amplitudes measured experimentally atV = +5 v andV = �5 v were 400 and�408�A, respectively.

The resistanceR placed in series with the power rails to facilitate experimental measurement of supply currents,I andI , is taken at a low value of

10.3. Therefore, the associated power dissipations,(�V ) =R and(�V ) =R , are negligible and therefore not included in these measurements.

Inferred fromP = P �P , which measures the difference in power consumed from the supplies and power dissipated in the 10-k resistive

loads when all 60 output drivers are active.

Duplicated from Table II.

the model. At each cell in the overlying grid, the discretizer de-termines the dominant tissue type occupying that cell and iden-tifies it according to the applied color segmentation. A uniquetissue identifier is assigned to each cell location which is usedas an index into a table of tissues (see Table IV) specifying di-electric and thermal properties. The resulting eye model that hasbeen discretized to a spatial resolution of 0.25 mm is shown inFig. 6(b).

A new 2-D head model was also constructed with a resolutionof 0.25 mm suitable for an accurate representation of the finestanatomical details of the human head. The head model is derivedfrom an image of the human head slice at a position intersectingthe eyes, taken from the National Library of Medicine (NLM)Visible Man Project[24]. As with the eye model, constructionof the head model proceeds by first color segmenting the headin order that tissues may be identified by uniform color. Sub-sequently, the discretizer is again used to sample the head sliceimage to a 0.25-mm model.

Since the eyes in the original head slice image from theVisibleMan Projectprovide only two or three discernible tissues, the0.25-mm resolution eye model separately developed is mergedwith the 0.25-mm head model to increase ocular detail as isshown in Fig. 7. A 2-D silicon model of the implanted stimulatorIC of dimensions 5.5 mm 5.25 mm is shown at midvitreousin the left eye, in the position and orientation associated withimplantation.

It is expected that temperature increase arising from inductivecoupling and from power dissipation in the stimulator IC willbe localized to the region of the eyes. Therefore, in order todecrease the required memory and simulation time, the head/eyemodel is truncated posterior to the eyes as shown in Fig. 8.

When computing SAR, the posterior edge of the model is im-mersed in the PML layers in order to correctly support the modeltruncation for the reduction of the computational space, as ex-plained in [16]. For the thermal simulation, instead, the initialsteady-state temperature distribution, which is computed in theabsence of any SAR and implant heating for the whole model,

is forced along the posterior boundary in order to prevent inap-propriate heat exchange with the surrounding environment. Themodel truncation is performed at a depth to which the conduc-tion of internal heat is expected to be negligible.

VII. PHYSICAL PROPERTIES OFTISSUES

Dielectric and thermal property values have been taken fromvarious publications collectively representing the research inelectromagnetic and thermal dosimetry. The dielectric proper-ties for the bodily tissues have been gathered from the DielectricProperties of Body Tissues online database [25]. These data arecompiled and organized by the Electromagnetic Wave ResearchInstitute of the Italian National Research Council (IROE-CNR),based on the work of Gabriel [26]–[30] dating back to 1996. Thepermittivities and conductivities are evaluated at 2 MHz cor-responding to the carrier frequency of the exterior transmittercoil in the inductive powering scheme. Thermal properties andspecific gravities for the biological tissues have been collectedprimarily from [31] released in 1990, but also from other pub-lications [8]–[10], [13], [15], [32]–[37]. OurRetina-3.5stimu-lator IC [20] fabricated in bulk CMOS is uniformly modeledwith the physical properties of intrinsic silicon available fromthe online elemental database [38]. These properties used withthe head/eye model are summarized in Table IV. As physicalproperties for some of the tissues are not explicitly available,values have been taken that match with tissues of nearest ex-pected composition or water content.

The newly developed eye model accounts for sclera, cornea,aqueous humor, pupillary sphincter muscle, posterior chamber,crystalline lens, lens zonules, cilliary muscle, vitreous humor,choroid, and retina. Pupillary and cilliary muscles, lens zonules(likened to tendons), and muscles attached to the sclera are rep-resented with the dielectric and thermal properties of generichuman muscle. Due to its close proximity, the posterior chambersituated between the lens and pupillary muscle takes its proper-ties from the aqueous humor. The permittivity and conductivity


(a)

(b)

Fig. 6. Discretization to obtain the 0.25-mm 2-D eye model. (a) Colorsegmentation according to tissue type. (b) 2-D eye model sampled to 0.25 mmusing a uniform grid.

of the aqueous humor at 2 MHz are taken as vitreous. Similarly,the mass density and thermal conductivity are shared amongthe aqueous and vitreous as [31] identifies a single humor forthese two properties. Moreover, the specific heat properties areequal, as in [13]. The highly vascularized choroid, which liesbetween the retina and sclera and nourishes the photoreceptors,is approximated with the physical properties of blood.

2http://www.btinternet.com/ms_pages/whitematter.html.3http://www.btinternet.com/ms_pages/greymatter.html.

Fig. 7. Merged model of the discretized head and eye models with inclusionof the silicon stimulator IC model in the left eye.

Fig. 8. Truncated model of the merged human head/eye models.

Only the dielectric properties of the retina have been foundin available research literature [25]; mass density and thermalproperties are not available. However, the retina is a multilayerneural structure approximately 300m thick with most of itscomposition organized as a cascade of various neuron celltypes and their interconnections [22], [39]–[41]. Only in theinnermost layer above the ganglion neurons is there a heavilyaxonal or nerve fiber layer. Therefore, in its composition, theretina is expected for the greater part to be analogous to braingray matter, where there is a higher concentration of neural cellbodies and dendrites.

White matter represents the portion of brain neural structureinvolved in communication between areas of gray matter andthus has a high nerve fiber, or axonal, composition. Furthermore,as the optic nerves are reported to contain white matter, physicalproperties of nerve are assumed similar to those of white matter.


TABLE IVDIELECTRIC AND THERMAL PROPERTIES OFTISSUES ANDMATERIALS IN THE HEAD/EYE MODEL AT 2 MHz

Dielectric properties" and� are taken from [25] unless otherwise noted.

Mass density� taken from [10] unless otherwise noted.

Blood perfusion constantB and basal metabolic rateA are taken from [9] unless otherwise noted.

Cortical bone, taken from [25].

Unavailable explicitly. Therefore, assigned the properties of aqueous humor.

Taken as muscle (generic).

Modeled as blood.

Human cortical bone, taken from [31].

Unavailable explicitly. Therefore, assigned the properties of brain white matter, as this is reported to have a high nerve fiber makeup and is contained in the

optic nerves.2

Human whole blood.

Taken from [13].

Human skeletal muscle, taken from [31].

Averaged human subcutaneous fat, taken from [31].

Taken from [8].

Human whole blood (43 % Hct), taken from [31].

Unavailable explicitly. Therefore, assigned the properties of brain gray matter, as this is reported to have a higher concentration of neural cell bodies and

dendrites than white matter.3

Unavailable explicitly. Therefore, assigned the properties of Vitreous Humor

Taken from [31].

Taken as Humor from [13].

Taken from [9].

Silicon not used in the calculation of the specific absorption rate.

Taken from [38].

The thermal conductivity of the implant is dependent on the precise material composition of the stimulator IC, any additional supporting intraocular compo-

nents, and the hermetically sealed biocompatible casing. Therefore, thermal simulations were conducted with values ofK 2 f10; 20;30; . . . ; 80;90g, so as

to characterize the dependence of temperature increase on the chip’s thermal conductivity. Subsequently, in order to minimize the computational time, temperature

rise associated withK = 150 (corresponding to the real value of silicon) are extrapolated according to the resulting trend.

Moreover, [9] and [42] report blood perfusion and basal metab-olism in agreement with that of brain, or white matter. Hence,physical properties for nerve in Table IV are assigned from thoseexplicitly available for white matter.

The thermal conductivity for the uniform silicon model ofour Retina-3.5stimulator IC [20] is reported from [38] as150 J ms C, which exceeds thermal conductivities of thebiological tissues by two order of magnitude. In accordance


with (4), this forces a smaller time step for stability and thus alonger simulation when compared with the case where siliconis absent from the model. The thermal conductivity of theimplant is dependent on the precise material compositionof the stimulator IC, any additional supporting intraocularcomponents, and the hermetically sealed biocompatible casing.Therefore, thermal simulations were conducted with valuesof , so as to characterize thedependence of temperature increase on the chip’s thermalconductivity. Subsequently, in order to minimize the compu-tational time, temperature rise associated with(corresponding to the real value of silicon) is extrapolatedaccording to the resulting trend.

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Stephen C. DeMarcowas born in Fairmont, WV, in1971. He received the B.S.(summa cum laude)andM.S. degrees in computer engineering from NorthCarolina State University, Raleigh, in 1994 and1996, respectively, where he is currently pursuingthe Ph.D. degree in electrical engineering.

His research is in the areas of analog/dig-ital/mixed-mode circuit design, VLSI, FPGAs, andcomputer vision/image-processing applicable toretina prosthesis development.


Gianluca Lazzi (S’94–M’95–SM’99) was bornin Rome, Italy, on April 25, 1970. He received theDr.Eng. degree in electronics from the Universityof Rome La Sapienza, Rome, Italy, in 1994 andthe Ph.D. degree in electrical engineering from theUniversity of Utah, Salt Lake City, in 1998.

He has been a Consultant for several companies(1988–1994), Visiting Researcher at the ItalianNational Board for New Technologies, Energy, andEnvironment (ENEA) (1994), Visiting Researcher

at the University of Rome La Sapienza (1994–1995), and Research Associate(1995–1998) and Research Assistant Professor (1998–1999) at the Universityof Utah. He is presently an Assistant Professor at the Department of Electricaland Computer Engineering, North Carolina State University, Raleigh. He isauthor or coauthor of more than 70 international journal articles or conferencepresentations on FDTD modeling, dosimetry, and bioelectromagnetics.

Dr. Lazzi received a 2001 NSF CAREER Award, a 2001 Whitaker Foun-dation Biomedical Engineering Grant for Young Investigators, a 1996 Interna-tional Union of Radio Science (URSI) Young Scientist Award, and the 1996Curtis Carl Johnson Memorial Award for the best student paper presented atthe eighteenth annual technical meeting of the Bioelectromagnetics Society. Heis an Associate Editor for the IEEE ANTENNAS AND WIRELESSPROPAGATION

LETTERS. He is listed inWho’s Who in the World, Who’s Who in America, Who’sWho in Science and Engineering, Dictionary of International Biographies,and2000 Outstanding Scientists of the 20th Century.

Wentai Liu (S’78–M’81–SM’93) received the Ph.D.degree in computer engineering from the Universityof Michigan at Ann Arbor in 1983.

He has been since 1983 on the Faculty of NorthCarolina State University, Raleigh, where he iscurrently the Alcoa Professor of Electrical and Com-puter Engineering. His research focuses on retinalprosthesis to restore eyesight for the blind, molecularelectronics, analog and digital VLSI design andCAD, phase-locked-loop, noise characterization andmodeling, timing/clock optimization, high-speed

transceiver for communication network, digital CMOS camera, telemetrydesign, and microelectronic sensor design.

Prof. Liu received an IEEE Outstanding Paper Award in 1986 and the AlcoaFoundation’s Distinguished Engineering Research Award in 1999.

James D. Weiland(S’92–M’99) received the B.S.degree, the M.S. degree in biomedical engineeringand electrical engineering, and the Ph.D. degreein biomedical engineering from the University ofMichigan, Ann Arbor, in 1988, 1993, 1995, and1997, respectively.

From 1997 to 2001, he was with the WilmerOphthalmological Institute, Johns Hopkins Univer-sity, first as a Postdoctoral Fellow and then as anAssistant Professor. In 2001, he became an AssistantProfessor in the Department of Ophthalmology,

University of Southern California Keck School of Medicine, Doheny EyeInstitute, Los Angeles, CA. His interests include retinal prostheses, electrodetechnology, visual evoked responses, and implantable electrical systems.

Dr. Weiland is a Member of the IEEE EMBS, the Biomedical EngineeringSociety, and the Association for Research in Vision and Ophthalmology.

Mark S. Humayun (M’97) received the M.D. de-gree from Duke University, Durham, NC, in 1989 andthe Ph.D. degree in biomedical engineering from theUniversity of North Carolina, Chapel Hill, in 1993.

He has been Assistant and Associate Professor atthe Department of Ophthalmology, Johns HopkinsHospital, Baltimore, MD. He is currently a Professorin the Department of Ophthalmology, Universityof Southern California Keck School of Medicine,Doheny Eye Institute, Los Angeles, CA.

Documents

Computed SAR and thermal elevation in a 0.25-mm 2 … · G. Lazzi was supported in part by the Whitaker Foundation under Contract RG-00-0298 and in part by NSF CAREER Award ECS-0091599